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The art of decomposition of a program into a set of functions is a pretty tricky are. One of the first discussion belongs to Parnas. He tried to demonstrate that it is almost always incorrect to begin the decomposition of a system into modules on the basis of a flowchart or program text (see "On the Criteria To Be Used in Decomposing Systems into Modules" published by the Communications of the ACM.). But after almost 30 years after the publication of the paper his suggestions looks somewhat naive (all he proposed is some lexical analysis of the sentences). In reality the creation of subroutines can be top-down or bottom up. In top down approach this is a process of factorization when you find repeatable patterns in programming code and generalize them into subroutine. In bottom up approach you create some abstract machine with higher level operations represented by subroutines and then try to write your solution in term of those abstract higher level operations (modifying and tuning them to the problem as your understanding of the task in hand improves). Parnas made a good point that the programmer who knows data structures and algorithms well is better than programmer who do not -- the former is able to approach problems from several paradigms and, for example, compiler construction is one such very powerful paradigm that can be used. Also see Summary of Design Readings for a short abstract and An Integrated Representation for Software Development and Discovery for a useful discussion).
Some subroutines are almost always present in most programs. For example the subroutine that prints and/or writes to a log file a warning or an error message is a typical example of "unique" subroutines. Die in Perl is an example of a primitive solution of this program within the language framework. Another one is the subroutine for analysis of input arguments passed to the program. Perl standard modules provide several solution to this problem.
In the past there was a special area computer science called modular programming that tried to study this program and refine the language features that made decomposition of the problem into subroutines easier and created subroutines less dependent upon each other. The idea of namespaces as a very important component of modularization came out of this research. It was the dominant approach to the "programming in large" before OO became fashionable.
Generally you want to organize your code into pieces that are easy to understand and work with and that are more or less separate from each other and communicate only using minimum number of variables. In practice, when you create your program from a simple prototype into full-blown production program, subroutines are often an afterthought because in a process of making the program more complex you notice that two fragments of code are similar enough to factor them into subroutines. And in version three or four of five your decomposition looks so ugly that you start plan to rewrite it but postponed it until version seven because codebase became too large ;-) In general modular programming can help you to hide the details so that readers of your source code can better understand the overall structure of your program, but good decomposition for a large problem is not easy to achieve.
In bastardized form the idea of creation of the catalog of classic decompositions within the OO paradigm is present in so called "programming pattern" movement.
Perl documentation contains a section called perlsub which is authoritative for the topic and should be read first.
A good publicly available introduction can be found in Learning Perl, 3rd Edition- Chapter 4- Subroutines. It does not cover the scope rules too well, though.
The other notable free source is Subroutines and References in Perl
There are also several valuable articles
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